1
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I have the adjacency matrix of graph and I want visualize this graph. I tried:

AdjacencyGraph[{v1,v2,v3,v4,v5,v6,v7,v8,v9,v10},
{{0,0,0,1,0,1,1,1,0,0},
 {0,0,0,0,0,1,1,1,1,1},
 {0,0,0,0,0,0,0,1,1,0},
 {1,0,0,0,0,0,0,1,0,0},
 {0,0,0,0,0,1,0,1,0,0},
 {1,1,0,0,1,0,1,0,1,1},
 {1,1,0,0,0,1,0,0,0,1},
 {1,1,1,1,1,0,0,0,0,1},
 {0,1,1,0,0,1,0,0,0,0},
 {0,1,0,0,0,1,1,1,0,0}}]

and

AdjacencyGraph[
{{0,0,0,1,0,1,1,1,0,0},
 {0,0,0,0,0,1,1,1,1,1},
 {0,0,0,0,0,0,0,1,1,0},
 {1,0,0,0,0,0,0,1,0,0},
 {0,0,0,0,0,1,0,1,0,0},
 {1,1,0,0,1,0,1,0,1,1},
 {1,1,0,0,0,1,0,0,0,1},
 {1,1,1,1,1,0,0,0,0,1},
 {0,1,1,0,0,1,0,0,0,0},
 {0,1,0,0,0,1,1,1,0,0}}]

Output is:

enter image description here

How to add names of vertices to graph?

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2
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VertexLabelsdoes the job.

AdjacencyGraph[{
{0, 0, 0, 1, 0, 1, 1, 1, 0, 0}, 
{0, 0, 0, 0, 0, 1, 1, 1, 1, 1},
{0, 0, 0, 0, 0, 0, 0, 1, 1, 0}, 
{1, 0, 0, 0, 0, 0, 0, 1, 0, 0},
{0, 0, 0, 0, 0, 1, 0, 1, 0, 0}, 
{1, 1, 0, 0, 1, 0, 1, 0, 1, 1}, 
{1, 1, 0, 0, 0, 1, 0, 0, 0, 1}, 
{1, 1, 1, 1, 1, 0, 0, 0, 0, 1}, 
{0, 1, 1, 0, 0, 1, 0, 0, 0, 0}, 
{0, 1, 0, 0, 0, 1, 1, 1, 0, 0}}, 
VertexLabels -> Table[i -> Subscript[v, i], {i, 10}]]

enter image description here

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3
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Similarily to the above:

Code:

g = {{0, 0, 0, 1, 0, 1, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 1, 1, 1, 
    1}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0}, {1, 0, 0, 0, 0, 0, 0, 1, 0, 
    0}, {0, 0, 0, 0, 0, 1, 0, 1, 0, 0}, {1, 1, 0, 0, 1, 0, 1, 0, 1, 
    1}, {1, 1, 0, 0, 0, 1, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 0, 0, 0, 0, 
    1}, {0, 1, 1, 0, 0, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 1, 1, 0, 
    0}};

AdjacencyGraph[g, VertexLabels -> "Name"]

Output:

Adjacency graph v.1

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AdjacencyGraph[
    {Labeled[v1, "1"],
     Labeled[v2, "2"],
     Labeled[v3, "3"],
     Labeled[v4, "4"],
     Labeled[v5, "5"],
     Labeled[v6, "6"],
     Labeled[v7, "7"],
     Labeled[v8, "8"],
     Labeled[v9, "9"],
     Labeled[v10, "10"]},
     {{0,0,0,1,0,1,1,1,0,0},
      {0,0,0,0,0,1,1,1,1,1},
      {0,0,0,0,0,0,0,1,1,0},
      {1,0,0,0,0,0,0,1,0,0},
      {0,0,0,0,0,1,0,1,0,0},
      {1,1,0,0,1,0,1,0,1,1},
      {1,1,0,0,0,1,0,0,0,1},
      {1,1,1,1,1,0,0,0,0,1},
      {0,1,1,0,0,1,0,0,0,0},
      {0,1,0,0,0,1,1,1,0,0}}]

enter image description here

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Add VertexLabels -> "Name" to your first command.

AdjacencyGraph[{v1,v2,v3,v4,v5,v6,v7,v8,v9,v10},
{{0,0,0,1,0,1,1,1,0,0},
 {0,0,0,0,0,1,1,1,1,1},
 {0,0,0,0,0,0,0,1,1,0},
 {1,0,0,0,0,0,0,1,0,0},
 {0,0,0,0,0,1,0,1,0,0},
 {1,1,0,0,1,0,1,0,1,1},
 {1,1,0,0,0,1,0,0,0,1},
 {1,1,1,1,1,0,0,0,0,1},
 {0,1,1,0,0,1,0,0,0,0},
 {0,1,0,0,0,1,1,1,0,0}},
 VertexLabels -> "Name"]

enter image description here

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